In this paper I consider an OLG model with production and a single commodity. I show that in such an environment unbounded growth of income per capita is not possible if the aggregate technology is of the usual constant returns to scale type. This is not due to lack of productivity of the capital stock in the long run but rather, to inappropriate distribution of income across generations, which makes it impossible for the young savers to afford buying the existing stock of capital. I then introduce an external effect, due to the stock of capital, in the aggregate production function and derive conditions under which persistent growth is an equilibrium outcome. I also show that the introduction of an external effect, while making growth feasible, also creates "poverty traps" and open sets of initial conditions for which there exists an infinite multiplicity of equilibria. I also show that, when such a multiplicity exists, equilibria with the very same initial position, will display remarkably different asymptotic behaviors. Finally I show that by introducing appropriate tax schemes such multiplicity can be eliminated but that the same is not true for poverty traps, which appears to be quite robust with respect to policy interventions.